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Classification of the Linearly Reductive Finite Subgroup Schemes of S L 2

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Abstract

We classify the linearly reductive finite subgroup schemes G of S L 2=S L(V) over an algebraically closed field k of positive characteristic, up to conjugation. As a corollary, we prove that such G is in one-to-one correspondence with an isomorphism class of two-dimensional F-rational Gorenstein complete local rings with the coefficient field k by the correspondence \(G\mapsto \left ((\mathrm {Sym\,}V)^{G}\right )\widehat {~}\).

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Authors and Affiliations

  1. Department of Mathematics, Okayama University, Okayama, 700–8530, Japan

    Mitsuyasu Hashimoto

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  1. Mitsuyasu Hashimoto
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Correspondence to Mitsuyasu Hashimoto.

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Dedicated to Professor Ngo Viet Trung on the occasion of his sixtieth birthday

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Hashimoto, M. Classification of the Linearly Reductive Finite Subgroup Schemes of S L 2 . Acta Math Vietnam 40, 527–534 (2015). https://doi.org/10.1007/s40306-015-0145-9

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  • DOI: https://doi.org/10.1007/s40306-015-0145-9

Keywords

Mathematics Subject Classification (2010)

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